Every so often a dog comes in with a swollen face. In fact, twice in a twelve-hour period this weekend I've seen a dog with a swollen face (different dogs, okay?) Look at that right lip and left eye. "What happened to him?" We don't know.
Dachshunds (more commonly than other breeds) sometimes get facial swelling as a part of a drug or vaccine reaction. It's like hives (urticaria for you scientific types). Some type of allergic reaction, we think.
Insect stings are probably the most common reason that dogs look like this. Again, an allergic-type reaction, but rarely as severe as the anaphylactic reactions that make your bronchial tubes swell shut. Those are the ones that cause you to quickly turn blue and die if you aren't carrying your epi-pen [a device for injecting a pre-measured dose of epinephrine, aka adrenaline — it opens them back up].
Snake-bites are a less common cause of facial swelling. In our part of the country, the only poisonous snakes we have to contend with are the copperhead and the cottonmouth. Dogs always investigate nose-first, so snake-bites almost always are on the front of the muzzle. The dog usually does not swell up anyplace else. When your basic mutt gets a face like a Shar Pei, think snake-bite.
Most of these would get okay eventually without much treatment. We give them antihistamines and cortisone, plus pain medicine if needed. The snakebites also should be treated like any other contaminated puncture wound (antibiotics). Unless there is respiratory distress, they really aren't emergencies. Of course, when it's your dog who is "blown up" they can sure look an emergency.